R for Art Sundays
Strange Attractors: General 2D Map - Part 1
An R experiment to create images generated by the trajectory of a particle according to a strange attractor.
Made with Rcpp, tidyverse
Blog post explaining the experiment: Rcpp, Camarón de la Isla and the Beauty of Maths
Inspired by: Strange Attractors: Creating Patterns in Chaos, by Julien C. Sprott
library(Rcpp)
library(tidyverse)
opt <- theme(legend.position = "none",
panel.background = element_rect(fill="white", color="black"),
plot.background = element_rect(fill="white"),
axis.ticks = element_blank(),
panel.grid = element_blank(),
axis.title = element_blank(),
axis.text = element_blank())
cppFunction('DataFrame createTrajectory(int n, double x0, double y0,
double a1, double a2, double a3, double a4, double a5,
double a6, double a7, double a8, double a9, double a10,
double a11, double a12, double a13, double a14) {
// create the columns
NumericVector x(n);
NumericVector y(n);
x[0]=x0;
y[0]=y0;
for(int i = 1; i < n; ++i) {
x[i] = a1+a2*x[i-1]+ a3*y[i-1]+ a4*pow(fabs(x[i-1]), a5)+ a6*pow(fabs(y[i-1]), a7);
y[i] = a8+a9*x[i-1]+ a10*y[i-1]+ a11*pow(fabs(x[i-1]), a12)+ a13*pow(fabs(y[i-1]), a14);
}
// return a new data frame
return DataFrame::create(_["x"]= x, _["y"]= y);
}
')
a1 <- -0.7157
a2 <- 0.3023
a3 <- 1.0129
a4 <- -0.036
a5 <- 0.2709
a6 <- 1.0922
a7 <- -0.7222
a8 <- -0.1647
a9 <- -0.4607
a10 <- -0.71570
a11 <- -0.71571
a12 <- -0.71572
a13 <- -0.71573
a14 <- -0.71574
df <- createTrajectory(10000000, 1, 1, a1, a2, a3, a4, a5, a6,
a7, a8, a9, a10, a11, a12, a13, a14)
mx <- quantile(df$x, probs = 0.05)
Mx <- quantile(df$x, probs = 0.95)
my <- quantile(df$y, probs = 0.05)
My <- quantile(df$y, probs = 0.95)
df %>% filter(x > mx, x < Mx, y > my, y < My) -> df
plot <- ggplot(df) +
geom_point(aes(x, y), shape=46, alpha=0.01, size=0, color="black") +
scale_x_continuous(expand = c(0,0))+
scale_y_continuous(expand = c(0,0))+
coord_fixed() +
opt
plot